New techniques in X-ray scattering science experiments produce large data sets that can require millions of high-performance processing hours per week of computation for analysis. In such applications, data is typically moved from X-ray detectors to a large parallel file system shared by all nodes of a petascale supercomputer and then is read repeatedly as different science application tasks proceed. However, this straightforward implementation causes significant contention in the file system. We propose an alternative approach in which data is instead staged into and cached in compute node memory for extended periods, during which time various processing tasks may efficiently access it. We describe here such a big data staging framework, based on MPI-IO and the Swift parallel scripting language. We discuss a range of large-scale data management issues involved in X-ray scattering science, and we measure the performance benefits of the new staging framework for high-energy diffraction microscopy, an important emerging application in data-intensive X-ray scattering. The use of our framework has been shown to accelerate scientific processing turnaround from three months to under 10 minutes, and our I/O technique reduces input overheads by a factor of 5 on 8K Blue Gene/Q nodes.